Shmotolokha V. Effects of porous media on thermodynamic properties and phase behavior of anisotropic fluids

The thesis is devoted to the development of theoretical approaches for the description of thermodynamic properties and phase behavior of anisotropic fluids in the bulk and in random porous media. Several models of anisotropic fluids (convex non-spherical particles, spherocylindrical particles) confined in a disordered porous medium are considered. Notably, special attention is given to anisotropic spherocylinder fluids. Analytical expressions for thermodynamic properties of such systems are obtained based on the scaled particle theory (SPT) generalized for anisotropic fluids. The results of the generalized theory are shown to be in good qualitative and quantitative agreement with computer simulations data. The SPT for anisotropic fluids in disordered media is used to describe the reference system in the framework of a perturbation theory for the study of vapor-liquid-nematic and vapor-nematic1-nematic2 phase transitions. An improved version of the generalized van der Waals equation for anisotropic fluids in disordered porous media is presented. The effect of a disordered porous medium on the phase behavior of these fluids is investigated. Lower porosity of the porous medium leads to a lower critical temperature and critical density as well as the narrowing of the vapor-liquid phase coexistence region. Effects of the porosity of the porous medium on the isotropic-nematic and nematic-nematic coexistence are studied. We show that the vapor-liquid phase transition can vanish due to the porous medium widening the isotropic–nematic phase transition. As the first step, the scaled particle theory is generalized to the case of non-spherical convex particles in a disordered porous medium. We study the effect of non-sphericity of fluid particles and the porosity of the porous medium on thermodynamic properties of such a system. Subsequently the role of attraction in anisotropic non-spherical fluids is investigated. The results obtained are tested against computer simulations data for the phase behavior of hard fluids in media of various sizes. A theory for the description of anisotropic molecular fluids with particles characterized by short-range repulsion is developed. The equation of state is generalized for anisotropic fluids in porous media based on the equation of state of hard spherocylindrical particles in a random porous medium derived in the framework of the SPT. Based on the equation obtained we investigate the isotropic-nematic phase behavior of molecular systems as a function of particle anisotropy as well as the porosity of the porous medium. We show that the porous medium lowers the density of the isotropic-nematic phase transition. The accuracy of the SPT2b1 is observed to decrease as the elongation of spherocylindrical particles decreases. Improvements to the SPT2b1 theory are proposed and, as a result, two different approaches are developed. The first one is the so-called SPT2b1-CS-PL approach which includes two corrections. One is the Carnahan-Starling correction which improves the description of thermodynamic properties at higher fluid densities. The second is the Parsons-Lee correction which improves the description of orientational ordering in a fluid of hard spherocylinders at high densities of the fluid. The phase diagram of a hard spherocylinder fluid in a disordered porous medium is calculated via two different methods. One approach is connected with the bifurcation analysis of the solution of a non-linear integral equation for the singlet distribution function obtained from the minimization of the free energy. Another approach is based on the condition of thermodynamic equilibrium. The numerical method proposed by J. Herzfeld and co-authors for the calculation of the bulk singlet function in systems with particle anisotropy and anisotropy of attractive interaction is generalized to account for the presence of a random porous medium. The phase diagrams obtained reveal that the critical parameters of a nematogenic fluid depend on the porosity of the medium, reproducing a known corresponding effect for simple spherocylinder fluids. Finally, using the SPT for the description of the reference system, the van der Waals equation is generalized and the phase behavior of a spherocylinder molecular fluid in a random porous medium is studied. The effect of the elongation of spherocylindrical particles on the isotropic-nematic coexistence is investigated. As particle elongation increases, a nematic-nematic phase transition is shown to emerge. The model proposed and the respective phase diagram are compared to the phase diagrams obtained for polypeptide solutions in dimethylformamide. The results obtained are shown to be in qualitative agreement with the experimental data for the polypeptide solutions in dimethylformamide.